Fun with Numbers - Calculating Motor Load Force

[MeticulousMaynard]

This is a topic that @pillageTHENburn and I were going into in a different thread, but I didn’t want to hijack it. I figured it’d be better etiquette to make a new thread.

I had mentioned:

@MeticulousMaynard

My sled is somewhere around the 40 lb mark and I haven’t run into any issues with the motors stalling. I need to more accurately measure its weight at some point, my current numbers come from adding together the weights of all the components. I have been wondering if I’m putting too much stress on the motors, though.

To which Logan responded, with actual formulas and stuff!

@pillageTHENburn

This could be because your motors are closer together right? The closer your motors are to each other the more acute the angle is between the chains when the sled is at top center (given the same motor height). The more acute that chain angle is the less tension there is on the chains.

That 39.5 pound number is based on “standard” machine dimensions (I don’t recall off the top of my head what numbers I used but I could look it up if you’re curious). The equation to find the force on two chains under load at a given angle is:
F = (m x 0.5) ÷ cos(a x 0.5)
where:
F is the calculated force on each chain
m is the mass or in our case the weight of the sled
a is the internal angle between the two chains

So if you measure your chain angle when the sled is top center you could plug in your numbers and figure out your max sled weight. (The max is 66 pounds per chain).

Thanks! This is one of those moments I really love our little community. Even if I don’t know the answer to a problem, someone else is more than willing to step in to provide!

I was at work when I posted my other reply, so I couldn’t get at my machine settings. Now that I’m home, I was able to open GC on my laptop and check my them. I drew up a quick diagram of the top beam of my machine in relation to the bed, and then overlaid the chains to mock up the position of the sled:

So, in the absolute, worst case scenario, if the bit was literally at the top of the bed, I would have 140.56 degrees of separation between the chains.

So to solve if:
m = 18 kg (~40 lbs)
a = 140.56 deg

F = (m x 0.5) ÷ cos(a x 0.5)

F = (18 x 0.5) ÷ cos(140.56 x 0.5)

F = 9 ÷ cos(70.28)

F = 9 ÷ 0.3374

F = 26.673 kg, or 58.8039 lbs.

So the load forces are 7 lbs lighter on my motors than the stock frame, which are cited around 65 lbs. I had initially been worried that I could be overloading the motors with my heavier sled, but after doing the math it doesn’t seem like that really is an issue.

The big take away from this is that I will have to be careful extending the length of the top beam and therefore the motor spacing. If I simply increase the beam length to 12 feet, my math says that will be 76 lbs at the motors, which is well beyond their stall load. So I would need to 1) raising the height of the beam, or 2) reduce the weight of the sled. I think that 2) would be the easiest solution to the problem, because reducing the sled to the stock 30 lbs puts ~60 lbs to the motors.

However, I think if greater accuracy is the goal, 1) would be the better solution to the problem. I can see there being a trade-off where adding too much height would introduce greater chain sag, so this may have to be tested to find its optimal ratio. But to me, I can image that in the areas where there are the most tension on the sled could introduce more error. So having the motors higher would reduce the amount of tension pulling at either side of the sled.

Or I’m completely off and we’ll all be laughing about this in an hour anyways

[dlang]

the areas where there is the most tension is the place where you are most sensitive to chain length. So if there is any flex in the system, you are going to see it here, and it will be magnified the most.

This is also where you need the highest resolution of the motor control (as small chain length changes translate into larger sled movement), but here the Maslow is overkill thanks to the encoder being before the gearbox.

So, assuming you have no flex in the system, there’s no problem with high tension areas.

going taller makes the angles to the bottom corners worse. Right now, I think that’s our biggest accuracy problem (assuming calibration and flex are solved)

So I would go wide and then go taller only if you find you have problems near the top center.

[MeticulousMaynard]

@dlang

So, assuming you have no flex in the system, there’s no problem with high tension areas.

This shouldn’t be a problem for a top beam frame. The only thing I’d really be worried about would be any play in the chain links, and any play in the linkage system. The latter shouldn’t be an issue, although if there is any slop in the system, the top of the machine is where we would notice them the most. I remember seeing posts that mentioned that there could be play in the chain links, which would obviously add up across a longer span of chain. Is this actually an issue or am I worrying over nothing?

@dlang

going taller makes the angles to the bottom corners worse. Right now, I think that’s our biggest accuracy problem (assuming calibration and flex are solved)

So I would go wide and then go taller only if you find you have problems near the top center.

That’s a very good point. So ultimately it may be the best idea to reduce the sled weight to prevent motor stall.

I wanted to make sure this is something we are thinking about as we go into experimenting with a longer top beam. I know that I wouldn’t think too much about it, go through all the effort of setting up a 12 or 14 foot beam, and then wonder why my motors can’t lift the sled. Admittedly, this probably affects me more than others, since I have a 40 lb sled currently.

[dlang]

@dlang

So, assuming you have no flex in the system, there’s no problem with high tension areas.

This shouldn’t be a problem for a top beam frame. The only thing I’d really be worried about would be any play in the chain links, and any play in the linkage system. The latter shouldn’t be an issue, although if there is any slop in the system, the top of the machine is where we would notice them the most. I remember seeing posts that mentioned that there could be play in the chain links, which would obviously add up across a longer span of chain. Is this actually an issue or am I worrying over nothing?

the answer is that we don’t know yet :-/